Elastic and Inelastic Analysis of Variable Thickness Plates, Using Equivalent Systems*

摘要

This paper develops a closed-form solution that can be used for both elastic and inelastic analysis of thin rectangular and circular plates with variable thickness in one dimension. The solution is given in the form of an equivalent system of flat plates that replaces the original variable thickness plate. At a given point, the sum of the deflections, rotations, bending moments, or bending stresses of the flat plates is equal to that of the corresponding elements of the original variable thickness plate. A simplified equivalent system of constant rigidity is also obtained, in order to reduce the mathematical complexity of the variable thickness problem. It should also be noted that any known method of analysis, closed-form or numerical, may be used to solve the equivalent system of flat plates. The method is general, and it can be applied equally well for both elastic and inelastic analysis. Various cases of loading and thickness variation are solved using both exact and simplified equivalent systems, and the results are compared. The plate is stressed well beyond the elastic limit of its material, all the way to failure. Conclusions are derived by observing the